The present invention relates to an apparatus and a method for image processing, a recording medium, and a program, and particularly to an apparatus and a method for image processing, a recording medium, and a program suitable for use in a case, for example, where the area of an arbitrary figure is divided by pixel units as equally as possible.
As shown in FIG. 1, for example, there are techniques for obtaining a number of pieces of two-dimensional image data by photographing a three-dimensional object from a number of positions on a circumference formed with the three-dimensional object as a center, and performing predetermined processing on the number of pieces of two-dimensional image data using a computer or the like to thereby generate three-dimensional image data of a given region including the three-dimensional object (region represented by a cylinder in FIG. 1 and hereinafter described as a reconstructing region).
The processing for generating the three-dimensional image data using the two-dimensional image data requires an enormous amount of storage of both space and calculation. Hence, when the processing is performed using a single calculator (such as a computer workstation), it takes a long time to obtain the three-dimensional image data as a result of the processing.
Thus, as described in literature such as “Toru Sasaki and Yasushi Fukuda: Reconstruction of Three-Dimensional X-Ray CT Image Using Distributed Memory Type Multiprocessor System, Information Processing Society of Japan, pp.1681, vol.38, No.9, September 1997” and “Feldkamp, L. A., Davis, L. C. and Kress, J. W.: Practical Cone-beam Algorithm, Optical Society of America, Vol.1, pp.612-619 (1984),” for example, a processing time required to obtain the three-dimensional image data may be reduced by dividing the reconstructing region in a vertical direction by a number of parallel lines, and making a parallel computer (or a number of independent computers) capable of performing a number of different computations simultaneously perform a computation for each of the divided regions.
When the reconstructing region is divided into a number of regions and different computers of the parallel computer are made to perform computations for the divided regions simultaneously, a method of dividing the reconstructing region is an important problem in reducing the processing time required to obtain the three-dimensional image data.
Suppose that the shape of a figure when the reconstructing region is viewed from a given direction is as shown in FIG. 2, for example. FIG. 3 shows an example of division of the reconstructing region. In the case of FIG. 3, the reconstructing region is divided into a number of regions equal to each other in width in a direction of the axis of abscissas (divided into six parts). Computations for the six divided regions S1 to S6 are performed by six computers P1 to P6 that perform parallel operation. In this case, as is clear from FIG. 3, areas of the regions S1 to S6 differ greatly from each other and, therefore, the computers P1 to P6 each have a different processing time (computation time), as shown in FIG. 4. Hence, the longest processing time, or the processing time of the computer P6 is a real processing time T1 of the computers P1 to P6 as a whole.
Next, FIG. 5 shows another example of division of the reconstructing region. In the case of FIG. 5, the reconstructing region is divided in a direction of the axis of abscissas (divided into six parts) such that areas of regions after the division are equal to each other. Computations for the six divided regions S1 to S6 are performed by six computers P1 to P6 that perform parallel operation. In this case, the areas of the regions S1 to S6 are equal to each other and, therefore, the processing times of the computers P1 to P6 are also equal to each other, as shown in FIG. 6. Hence, a real processing time T2 of the computers P1 to P6 as a whole is shorter than the real processing time T1 of the computers P1 to P6 as a whole in the case of FIG. 3.
It is easy to geometrically divide an arbitrary figure in the direction of the axis of abscissas such that areas of regions after the division are equal to each other, as shown in FIG. 5. In practice, however, image data of the reconstructing region is formed by pixel units. A dividing boundary line is therefore limited to a position between pixels; in other words, the division needs to be made by pixel units. However, it is difficult to divide an arbitrary figure by pixel units in the direction of the axis of abscissas such that areas after the division are equal to each other, and no techniques for this have been established.